scholarly journals Approximating Fixed Points of Reich–Suzuki Type Nonexpansive Mappings in Hyperbolic Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Kifayat Ullah ◽  
Junaid Ahmad ◽  
Manuel De La Sen ◽  
Muhammad Naveed Khan
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Iterative Process ◽  
Fixed Point Theory ◽  
Nonexpansive Mappings ◽  
Point Theory ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Convergence Results ◽  
Hyperbolic Metric Space

In this work, we prove some strong and Δ convergence results for Reich-Suzuki type nonexpansive mappings through M iterative process. A uniformly convex hyperbolic metric space is used as underlying setting for our approach. We also provide an illustrate numerical example. Our results improve and extend some recently announced results of the metric fixed-point theory.

scholarly journals Fixed Point Approximation of Nonexpansive Mappings on a Nonlinear Domain

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Safeer Hussain Khan
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Hyperbolic Space ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Convergence Results ◽  
Uniformly Convex Banach Spaces ◽  
Uniformly Convex Hyperbolic Space

We use a three-step iterative process to prove some strong andΔ-convergence results for nonexpansive mappings in a uniformly convex hyperbolic space, a nonlinear domain. Three-step iterative processes have numerous applications and hyperbolic spaces contain Banach spaces (linear domains) as well as CAT(0) spaces. Thus our results can be viewed as extension and generalization of several known results in uniformly convex Banach spaces as well as CAT(0) spaces.

scholarly journals Numerical reckoning fixed points for Suzuki’s generalized nonexpansive mappings via new iteration process

Filomat ◽  
2018 ◽  
Vol 32 (1) ◽  
pp. 187-196 ◽  
Author(s):  
Kifayat Ullah ◽  
Muhammad Arshad
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Fixed Points ◽  
Fixed Point Theory ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Point Theory ◽  
Uniformly Convex ◽  
Weak And Strong Convergence ◽  
Uniformly Convex Banach Spaces

In this paper we propose a new three-step iteration process, called M iteration process, for approximation of fixed points. Some weak and strong convergence theorems are proved for Suzuki generalized nonexpansive mappings in the setting of uniformly convex Banach spaces. Numerical example is given to show the efficiency of new iteration process. Our results are the extension, improvement and generalization of many known results in the literature of iterations in fixed point theory.

Some convergence results for nonexpansive mappings in uniformly convex hyperbolic spaces

2017 ◽  
Vol 26 (3) ◽  
pp. 331-338
Author(s):  
AYNUR SAHIN ◽  
◽  
METIN BASARIR ◽  
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Hyperbolic Space ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Convergence Results ◽  
Uniformly Convex Hyperbolic Space

In this paper, we establish some strong and 4-convergence theorems of an iteration process for approximating a common fixed point of three nonexpansive mappings in a uniformly convex hyperbolic space. The results presented here extend and improve various results in the existing literature.

scholarly journals Iterative Construction of Fixed Points for Operators Endowed with Condition E in Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Junaid Ahmad ◽  
Kifayat Ullah ◽  
Hüseyin Işik ◽  
Muhammad Arshad ◽  
Manuel de la Sen
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Iterative Process ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Uniformly Convex ◽  
Uniformly Convex Hyperbolic Space ◽  
Iterative Procedures ◽  
Iterative Construction

We consider the class of mappings endowed with the condition E in a nonlinear domain called 2-uniformly convex hyperbolic space. We provide some strong and Δ -convergence theorems for this class of mappings under the Agarwal iterative process. In order to support the main outcome, we procure an example of mappings endowed with the condition E and prove that its Agarwal iterative process is more effective than Mann and Ishikawa iterative processes. Simultaneously, our results hold in uniformly convex Banach, CAT(0), and some CAT( κ ) spaces. This approach essentially provides a new setting for researchers who are working on the iterative procedures in fixed point theory and applications.

scholarly journals Existence and approximation of a fixed point of a fundamentally nonexpansive mapping in hyperbolic spaces

2020 ◽  
Vol 36 (1) ◽  
pp. 71-80
Author(s):  
HAFIZ FUKHAR-UD-DIN
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Common Fixed Point ◽  
Hyperbolic Space ◽  
Convex Subset ◽  
Fixed Point Theory ◽  
Nonexpansive Mappings ◽  
Point Theory ◽  
Hyperbolic Spaces ◽  
One Step

We prove that a fundamentally nonexpansive mapping on a compact and convex subset of a hyperbolic space, has a fixed point. We also show that one-step iterative algorithm of two mappings is vital for the approximation of a common fixed point of two fundamentally nonexpansive mappings in a strictly convex hyperbolic space. Our results are new in metric fixed point theory and generalize several existing results.

scholarly journals Fixed Point Approximation for Asymptotically Nonexpansive Type Mappings in Uniformly Convex Hyperbolic Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Shin Min Kang ◽  
Samir Dashputre ◽  
Bhuwan Lal Malagar ◽  
Young Chel Kwun
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Iterative Process ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Point Approximation ◽  
Convergence Results ◽  
Asymptotically Nonexpansive

We use a modifiedS-iterative process to prove some strong andΔ-convergence results for asymptotically nonexpansive type mappings in uniformly convex hyperbolic spaces, which includes Banach spaces and CAT(0) spaces. Thus, our results can be viewed as extension and generalization of several known results in Banach spaces and CAT(0) spaces (see, e.g., Abbas et al. (2012), Abbas et al. (2013), Bruck et al. (1993), and Xin and Cui (2011)) and improve many results in the literature.

scholarly journals Semicompatibility and fixed point theorems in an unboundedD-metric space

2005 ◽  
Vol 2005 (5) ◽  
pp. 789-801
Author(s):  
Bijendra Singh ◽  
Shishir Jain ◽  
Shobha Jain
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Condition ◽  
Restricted Domain

Rhoades (1996) proved a fixed point theorem in a boundedD-metric space for a contractive self-map with applications. Here we establish a more general fixed point theorem in an unboundedD-metric space, for two self-maps satisfying a general contractive condition with a restricted domain ofxandy. This has been done by using the notion of semicompatible maps inD-metric space. These results generalize and improve the results of Rhoades (1996), Dhage et al. (2000), and Veerapandi and Rao (1996). These results also underline the necessity and importance of semicompatibility in fixed point theory ofD-metric spaces. All the results of this paper are new.

scholarly journals Transfinite methods in metric fixed-point theory

2003 ◽  
Vol 2003 (5) ◽  
pp. 311-324 ◽  
Author(s):  
W. A. Kirk
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Nonexpansive Mappings ◽  
Point Theory ◽  
Transfinite Induction ◽  
Caristi’S Theorem ◽  
Countable Compactness ◽  
Recent Extension

This is a brief survey of the use of transfinite induction in metric fixed-point theory. Among the results discussed in some detail is the author's 1989 result on directionally nonexpansive mappings (which is somewhat sharpened), a result of Kulesza and Lim giving conditions when countable compactness implies compactness, a recent inwardness result for contractions due to Lim, and a recent extension of Caristi's theorem due to Saliga and the author. In each instance, transfinite methods seem necessary.

On a theorem of Brian Fisher in the framework of w-distance

2017 ◽  
Vol 33 (2) ◽  
pp. 199-205
Author(s):  
DARKO KOCEV ◽  
◽  
VLADIMIR RAKOCEVIC ◽  
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Complete Metric Space ◽  
Point Theory ◽  
Common Fixed Points ◽  
Complete Metric Spaces ◽  
Condition C ◽  
Relaxing Condition

In 1980. Fisher in [Fisher, B., Results on common fixed points on complete metric spaces, Glasgow Math. J., 21 (1980), 165–167] proved very interesting fixed point result for the pair of maps. In 1996. Kada, Suzuki and Takahashi introduced and studied the concept of w–distance in fixed point theory. In this paper, we generalize Fisher’s result for pair of mappings on metric space to complete metric space with w–distance. The obtained results do not require the continuity of maps, but more relaxing condition (C; k). As a corollary we obtain a result of Chatterjea.

Sign in / Sign up

Export Citation Format

Share Document